Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Fractals”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8Linked to original sources
PubMed2001

Fractal dimension analysis of static stabilometry in Parkinson's disease and spinocerebellar ataxia.

The static stabilometry patterns associated with Parkinson's disease (PD, n = 15) and spinocerebellar ataxia (SCA, n = 15) were compared with those of normal control (n = 15) by measuring the fractal dimensions. Fractal dimensions were estimated using the modified pixel dilation (mPD) method. The fractal dimensions with closed eyes showed a significant correlation with Environmental area for SCA group (p < 0.05). The fractal dimension for SCA group was significantly higher with closed eyes than that with open eyes (p < 0.05). The fractal dimension with closed eyes was significantly higher in PD and SCA groups than that in normal group (p < 0.05). The fractal dimension with closed eyes was higher when the clinical stage was more severe with PD and SCA group while Environmental and Longitude/Environmental areas were not. These findings suggest that the fractal dimension is more sensitive than traditional stabilometric analysis in an evaluation of postural instability in PD and SCA.

Aged↗
PubMed1998

Fractal dimension as a measure of altered trabecular bone in experimental inflammatory arthritis.

Our previous studies in experimental inflammatory arthritis (EIA) and in human rheumatoid arthritis demonstrated rapid remodeling with a 5-fold increase in bone resorption and bone formation. Normal condylar trabecular bone is typically anisotropic, with its orientation along lines of stress; rapid remodeling in a pathological state could disturb the usual order of trabeculae. This study assessed change in the structure of trabecular bone of the distal femoral epiphysis after induction of EIA, using a measure of "fractal dimension," which may be considered a quantitative description of the degree of irregularity of complex surfaces. Data was obtained from specimens in which EIA had been induced in the rabbit knee by 10 injections of carrageenan over 49 days. Photographic enlargements of embedded undecalcified cross-sections of the distal femur were digitized, and software written on a Sun workstation was used to define repeatable regions of interest (ROIs) in the images. The ROIs were subjected to fractal analysis by a power law method. The fractal dimension of the trabecular bone pattern within the ROI was estimated by fitting an equation of the form A (epsilon) = lambda epsilon (2-D) to the data. In this equation, A (epsilon) is the area of the "surface" formed by modeling the ROI data as a three-dimensional structure with the grey-level magnitude providing the third dimension, lambda is a scaling constant, epsilon is the size of the measuring "tool" used to measure the area, and D is the fractal dimension. A Mann-Whitney U-test applied to the average of the data from all ROIs showed that the two distributions of fractal dimension were significantly different (p < 0.005). There were only two overlaps between data points for arthritis (with these values higher) and normal groups (n = 11 for each group). Since Howship's lacunae were too small to be resolved in the system utilized, we consider the difference in fractal dimension to be primarily related to trabecular surface orientation, rather than to the increased number of asperities (resorptive foci) occurring due to increased turnover in bone affected by inflammatory arthritis. The results suggest that fractal dimension may be a useful tool for assessing the degree of structural damage to trabeculae in conditions similar to EIA.

Animals↗
PubMed2003

[Complexity evaluation of data transfer in the Z-axis direction in 4-row multislice spiral CT using fractal dimension analysis].

Image reconstruction in multislice spiral/helical computed tomography (MSCT) consists of a package of data on the arbitrary direction of the Z-axis that can be collected by active detector arrays. Thus the recombined data vary with each spiral pitch. In certain cases of spiral pitch, data compression can occur, and the spiral artifacts that are characteristic of MSCT would change. In our study, we evaluated image complications by fractal dimensions, because the geometrical patterns from a conic phantom are closely related to data transfer in the direction of the Z-axis in spiral pitches. We hoped to establish useful spiral pitches and slice collimation for clinical use in a 4-row MSCT scanner. By employing a conic phantom of 120 mm in diameter and a cone angle of 100 degrees, we measured the fractal dimension of the conic phantom image by making a binary to outline from 2.0 to 8.0 of various slice collimations. Moreover, in order to evaluate the correlation between fractal dimensions and image artifacts, we confirmed the influence of spiral pitch and reconstruction slice thickness for clinical use. We found that, when the reconstruction slice thickness was the same, the cross section of the conic phantom that was from thin-slice collimations was more similar to an actual circle than that of wide-slice collimations. The former deserved a low value and showed slight changes, and, therefore, its fractal dimensions were fixed. As a phenomenon worthy of attention, when we employed wide-slice collimations (4x5.0 mm) during peculiar low spiral pitches of 2.5 to 3.0 fractal dimensions remained low and similar to an actual circle. By these analyses of the influence of data transfer in the direction of the Z-axis, we found that spiral pitch influenced the rate of slice collimation used for data acquisition closely to the reconstruction slice thickness. Based on these findings, when slice collimations and reconstruction slice thickness should be made equal, we estimated that spiral pitches of low image artifacts in 4row MSCT ranged from 2.5 to 3.0 using fractal dimensions. We consider that a new adaptation of fractal dimension analysis is possible when it is used as an index in determining protocols.

Artifacts↗
PubMed1998

[The evaluation of umbilical arterial Doppler spectrum fractal characterization in obstetrics].

OBJECTIVE: To evaluate the clinical value of fetal umbilical arterial Doppler spectrum fractal. METHODS: 104 cases with 22-41 gestational weeks were included, and divided into two groups: normal pregnant group, 59 cases; abnormal pregnant group, 45 cases. Umbilical arterial Doppler spectrum were obtained by color Doppler ultrasound, then Doppler signal were transformed into computer through sound-frequency, and fractal were calculated. RESULTS: The fractal was 1.83 +/- 0.03 in normal pregnant group. The frequency of abnormal fractal was significantly higher in abnormal pregnant group than that in normal pregnant group (P < 0.001). Compared with the ratio of peak systolic to lowest diastolic flow velocity (S/D), the fractal was more sensitive than S/D ratio in abnormal pregnancy (P < 0.05). There were significant correlation between fractal and gestational weeks (r = 0.266). CONCLUSION: Fractal responses to complexity of umbilical arterial blood flow, and it is a better parameter than S/D ratio in monitoring abnormal umbilical arterial blood flow.

Adult↗
PubMed2003

[Fractal relationship between above ground biomass and plant length or sheath height of Carex lasiocarpa population].

By using the principles and methods of fractal geometry theory, the relationship between above ground biomass and plant length or sheath height of Carex lasiocarpa population was studied. The results showed that there was a good static fractal relationship between them, and the resulted fractal dimension was an efficient description of the accumulation of above ground biomass in each organ. The dynamic fractal relationship showed that during the whole growing season, the increase of above ground biomass had a self-similarity, being a fractal growth process, and the pattern of its increase was the fractal dimension D. Based on these results, a fractal growth model of Carex lasiocarpa population was established, which regarded the bigger grass as the result of the amplification of seedling growth.

Biomass↗
PubMed2004

Fractal dimension in endometrial carcinoma.

OBJECTIVE: To mathematically assess in a pilot study, endometrial glandular margin irregularity in simple hyperplasia, complex atypical hyperplasia and well-differentiated endometrial carcinoma with the help of box counting of fractal dimension and to discriminate these lesions on the basis of box counting of fractal dimension of the gland. STUDY DESIGN: Ten cases each of endometrial simple hyperplasia (without atypia), complex hyperplasia with atypia and endometrial carcinoma (well-differentiated, endometrioid) were assessed in the study. Five fields at 20 x magnification from each case were randomly selected, and the glands were outlined with the help of a pointer. Using the box counting method, the fractal dimension of each case was measured. RESULTS: Mean fractal dimension in simple hyperplasia, complex atypical hyperplasia and endometrial carcinoma was, 0.899 +/- 0.13, 0.932 +/- 0.042 and 0.939 +/- 0.02, respectively. Statistical analysis showed that the fractal dimension of glands of simple hyperplasia were significantly different from that of complex atypical hyperplasia and endometrial carcinoma (P = .041 and .013, respectively, ANOVA). However, there was no significant difference in fractal dimension between glands of complex hyperplasia and of endometrial carcinoma (P = .659, ANOVA). CONCLUSION: This study provides mathematical (objective) assessment of the measurement of glandular margin irregularities in simple hyperplasia, complex atypical hyperplasia and endometrial carcinoma. Fractal dimension of gland margin may have diagnostic potential in the future.

Endometrial Hyperplasia↗
PubMed2005

Perceptual and physiological responses to the visual complexity of fractal patterns.

Fractals have experienced considerable success in quantifying the complex structure exhibited by many natural patterns and have captured the imagination of scientists and artists alike. With ever widening appeal, they have been referred to both as "fingerprints of nature" and "the new aesthetics." Our research has shown that the drip patterns of the American abstract painter Jackson Pollock are fractal. In this paper, we consider the implications of this discovery. We first present an overview of our research from the past five years to establish a context for our current investigations of human response to fractals. We discuss results showing that fractal images generated by mathematical, natural and human processes possess a shared aesthetic quality based on visual complexity. In particular, participants in visual perception tests display a preference for fractals with mid-range fractal dimensions. We also present recent preliminary work based on skin conductance measurements that indicate that these mid-range fractals also affect the observer's physiological condition and discuss future directions based on these results.

Arousal↗
PubMed2005

Basic principles and applications of fractal geometry in pathology: a review.

The basic principles and prospects of fractal geometry in pathology are promising. All articles found with a PubMed search with the keywords fractal dimension (FD) and related to pathology were reviewed. All fractal objects have FDs, commonly calculated with box counting. Fractal geometry has been applied to measure the irregularities of nuclear and glandular margins to distinguish malignant lesions from benign ones, to measure the infiltrative margin of a malignant tumor, to assess tumor angiogenesis and to measure the distribution of collagen in tissue. Fractal geometry has also been applied to assess the irregular distribution of chromatin in malignant cells. Biologic model formation is possible with fractal geometry. In the future, fractal geometry may help with the diagnosis, understanding of pathogenesis and management of lesions. It may also provide new insights into disease processes.

Animals↗
PubMed1995

Can the artificial heart make the circulation become fractal?

In order to analyze the hemodynamic parameters in prosthetic circulation as an entity and not as decomposed parts, non linear mathematical analyzing techniques, including the fractal dimension analyzing theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted, as biventricular bypasses (BVB), in chronic animal experiments, using four healthy adult goats. For the comparison between the natural and prosthetic circulation in the same animals, the BVB type complete prosthetic circulation model with ventricular fibrillation, was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions, and calculated with a personal computer system. Using the non-linear mathematical technique, the arterial blood pressure waveform was embedded into the return map as the beat-to-beat time series data and fractal dimension analysis were performed to analyze the reconstructed attractor. By the use of the Box counting method, fractal dimension analysis of the hemodynamics was performed. Return map of the hemodynamics during natural and artificial circulation showed fractal characteristics, and fractal dimension analysis of the arterial blood pressure revealed the fact that lower dimensional fractal dynamics were evident during prosthetic circulation. Fractal time series data is suggested to have robustness and error resistance, thus our results suggest that the circulatory regulatory system with an artificial heart may have these desired characteristics.

Animals↗
PubMed1998

[Fractal analysis of a breast carcinoma--presentation of a modern morphometric method].

Fractal analysis techniques are common tools in physics and image processing. In the past few years they have gained increasing attention in medical sciences, e.g., cardiology, pathology and radiology, respectively. This article intends to describe this new technique by applying fractal analysis to the instant of a breast carcinoma. One of the advantages of fractal analysis is the ability to describe an irregular and complex object by a measureable value, called the fractal dimension. The fractal dimension can be determined by using the box-counting method. We applied this technique to the mammography as well as to the histologic section of a breast carcinoma. The application of fractal analysis provides a specific measureable value of the growth pattern of a tumor. Thus, the fractal dimension serves in addition to the common used metric diameter.

Aged↗
PubMed2000

An Evaluation of Cellular Analyte-Receptor Binding Kinetics Utilizing Biosensors: A Fractal Analysis.

A fractal analysis is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using (a) a single-fractal analysis and (b) a single- and a dual-fractal analysis. Case (b) represents a change in the binding mechanism as the reaction progresses on the biosensor surface. Relationships are presented for the binding rate coefficient(s) as a function of the fractal dimension for the single-fractal analysis examples. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. For example, for the binding of mutagenized and back-mutagenized forms of peptide E1037 in solution to salivary agglutinin immobilized on a sensor chip, the order of dependence of the binding rate coefficient, k, on the fractal dimension, D(f), is 13.2. It is of interest to note that examples are presented where the binding coefficient (k) exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist us in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficients (or affinities). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensors or other surfaces. Copyright 2000 Academic Press.

Journal Article↗
PubMed2005

Fractal structure of asphaltene aggregates.

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.

Journal Article↗
PubMed2002

Modeling coagulation kinetics incorporating fractal theories: comparison with observed data.

There are currently four possible approaches in modeling coagulation kinetics: the traditional Euclidean rectilinear; the Euclidean curvilinear; the fractal rectilinear; and the fractal curvilinear. The fractal model includes the Euclidean case as a subset. The primary purpose of this research is to investigate which of the rectilinear models among these best predicts the evolution of experimental observed particle size distribution (PSD). Using a fractal rectilinear model previously developed by the authors, model predictions were compared with a series of observed PSD data obtained from estuarine sediment particles in a 2m settling column, where the average velocity gradient (G) was 20 or 40s(-1). Nonlinear parameter estimation was performed to estimate two free parameters for the fractal model (the fractal dimension, DF, and the collision efficiency factor, a), and one free parameter (the collision efficiency factor, alpha) for the Euclidean model. Compared with the observed PSD, the simulation showed that the fractal rectilinear model was best, and that this model fit better for the larger size particles. The estimated DF was between 2.6 and 3.0. The research demonstrated that the alpha's have multiple values for the same observed data, depending on the coagulation model used. This finding is significant because a is currently used as a single value based on the conventional Euclidean rectilinear model.

Geologic Sediments↗
PubMed1998

Effect of fractal dimension on drug permeation through porous ethylcellulose films.

Fractal geometry was applied to quantify the complexity of an internal structure of a porous film prepared with ethylcellulose (EC) and diethylphthalate (DEP) as a plasticizer. EC was dissolved together with DEP in a water-ethanol mixture solution, and then evaporated on Teflon petri dishes in order to make porous EC films. Boundary lines of the porous structures in the EC film cross section were taken by a confocal laser microscope as image data, and these images were fed into a computer to estimate the fractal dimension. The porous structure in EC film was observed to be a typical fractal and its complexity was quantified as a non-integral fractal dimension. No clear correlation was observed between the fractal dimension and the porosity of EC films, suggesting that they were mutually independent parameters representing the porous structure in the EC films. The permeation of theophylline through the EC films was determined by using two-chamber diffusion cells. A fairly good relationship between the permeability coefficient of theophylline and the fractal dimensions was observed, suggesting the usefulness of the fractal dimension as a novel parameter for evaluating drug permeation through porous films.

Cellulose↗
PubMed2005

Multiple rate-determining steps for nonideal and fractal kinetics.

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.

Journal Article↗
PubMed2007

Spontaneous formation of fractal structures on triglyceride surfaces with reference to their super water-repellent properties.

Alkylketene dimer (AKD), a kind of wax, has been known to form fractal surfaces spontaneously and show super water-repellency. Such formation of water-repellent and fractal surfaces was also found in this work for triglycerides. Since the crystal phase transitions of these waxes were well studied, we studied the formation of their fractal surfaces through contact angle measurements, differential scanning calorimetry (DSC), and X-ray diffraction (XRD). From time-dependent contact angle measurements, it was found that the formation of super water-repellent surfaces with fractal structures occurred spontaneously also on the triglyceride surfaces at different temperatures. The freshly solidified triglyceride surfaces were almost transparent, and their initial contact angles of water were close to 110 degrees. The surfaces then became rough and clouded after being incubated for a certain time at a specified temperature. The super water-repellent surfaces were quite rough and showed fractal structures with the dimension of ca. 2.2 calculated from the scanning electron microscopic (SEM) images by the box-counting method. The phase transformation from a metastable state to a stable cystalline one after the solidification from the melt of triglycerides was clearly observed by DSC and XRD measurements. The fractal crystalline structures and the super water-repellency resulted from this phase transformation and the crystal growth. Ensuring the initial sample solidified into the metastable state and curing the surface at an appropriate temperature are key factors for the successful preparation of fractal triglyceride surfaces by the solidification method.

Journal Article↗
PubMed1992

Fractal organisation in biological macromolecular lattices.

Macromolecular solutions of proteic, glycoproteic or polysaccharidic nature in the presence of salt gave rise (when slowly dried) to dendritic-like fractal patterns. A fractal dimension D = 1.79 +/- 0.018 was obtained for dendritic patterns of a sonicated ovomucin gel (40% ovomucin-60% ovalbumin) in the presence of 0.1 M NaCl. The calculated D is similar to that described in percolation clusters. The appearance of fractal patterns was dependent upon the protein:salt ratio with an optimum in the range 0.75-1.25. Patterns disappeared at either lower or higher ratios. We conclude that the salt percolates through the macromolecular lattice and precipitates in fractal clusters during the drying process. Dendritic-like fractal patterns with similar D and morphologies were obtained with solutions of fetuin, ovalbumin, albumin or starch suggesting that fractal patterning is a general property of biological polymers. That cellular polymers would also aggregate in a fractal way was implied from the analysis of cellular cytoskeleton and microtrabecular lattices.

Glycoproteins↗
PubMed2004

Effects of fill time on the fractal dimension and size of floc for SBR treating low C/N ratio wastewater.

The aim of this study was to investigate the effects of fill time of influent on the physical characteristics of biological floc for sequencing batch reactor (SBR) treating low C/N ratio wastewater. The fractal dimension and size of floc were measured for characterizing floc. The fractal dimension of floc was analyzed by using Small Angle Laser Light Scattering (SALLS) method. SBR with short fill time showed higher removal efficiencies of COD, BOD, T-N, and T-P than with long fill time. Larger floc size and fractal dimension were generated at SBR with short fill time. Short fill time generated the sludge with better settling and thickening properties. Alternating anaerobic and aerobic condition in the cycle also affected the floc size and fractal dimension. The floc size decreased under anaerobic phase, and floc size increased under aerobic phase. During fill time, the fractal dimension of floc decreased. As the fill stop, the fractal dimension of floc increased. Therefore, the fill time condition more affected the fractal dimension of floc. More efficient nitrification and phosphorus release were observed during a cycle with short fill time operation.

Bacteria, Aerobic↗